Someone on /r/canadapolitics asked for an introduction to Canadian politics, at the ELI5 (explain like I'm five) level.
1. Taxation and public spending as collective shopping - Scarry
Okay, I'm going to start by taking you literally: The best explanation I've seen for five-year-olds is the story "Building a new road" in Richard Scarry's What Do People Do All Day?
In the story, two towns (Busytown and Workville) are connected by a unpaved, bumpy, dusty road. It's terrible. They decide they want to build a new one. So the mayors of the two towns show up in the office of a road builder, each carrying a sack of tax money, with an explanation of what they want. (The rest of the story, of course, is devoted to the mechanics of building a road, complete with illustrations of various earthmoving machines.)
A surprising amount of what governments do is along these lines. Some goods and services, like food, clothing, and housing, we buy individually. Others - roads, schools, health insurance, public pensions - we buy collectively, by pooling our money through taxes. These tend to be goods and services that are shared, and where most people need pretty much the same thing. A one-page explanation of the benefits from risk-pooling.
2. The monopoly on the legitimate use of violence - Hobbes
In Canada we tend to take our personal security for granted, but there's a lot of places in the world where violence is a big problem. Why is that? Why can't everyone just get along?
Historically, the philosopher who explained the problem is Hobbes. I like Andrew Schmookler's version of it: Imagine that you have a bunch of neighboring tribes living peacefully. As long as they're all peaceful, that's fine. But imagine that one of the tribes decides to conquer all the others by force. At that point the other tribes can submit (adding to the power of the conqueror), flee (making room for the conqueror to expand), or take up arms themselves and resist violently. No matter what they choose, power and violence spread through the system. It's inescapable.
Even slugs are territorial. They fight battles (at twice their normal speed) over territory.
So a major role of government is external security (diplomacy, trade, military) and internal security (police and emergency services).
Historically speaking, Canada is a successor-state of the British Empire. We're a pluralistic, multinational state, like the Austro-Hungarian Empire, incorporating both English- and French-speakers, Protestants and Catholics, from the very beginning. Perhaps this is why it's been relatively easy for Canada to integrate newcomers, compared to more monolithic societies.
Ultimately authority depends on consent. Canadians complain about taxes, but they pay them: the government doesn't need to send armed CRA agents to every household to collect taxes. Where people have strong grievances and consent is weak - with the First Nations, sometimes with Quebec - you can expect trouble.
(As an aside, it's human nature to resent other people's power over you, while feeling that one's own power over others is natural and just. Thus Canadians tend to resent American power, while dismissing the grievances of First Nations and Quebec nationalists: "Why are they always complaining?")
The big divide in international politics is between those powers which support the international status quo and those which oppose it. Generally speaking, Canada supports the international status quo - we have a strong interest in peace, stability, and trade - which is why Canada fought in World War I and II, opposed the Soviet Union during the Cold War, and why we're a member of NATO today. (The NATO treaty is a treaty of mutual defense: each member is committed to treating an attack on any member as an attack on itself. In particular, this commits the US to the defense of Europe against Russia.)
3. Rules and regulations
A great deal of economic and social life depends on norms - basically rules which define what you're not supposed to do, along with sanctions for violating them. These sanctions may be moral (you feel bad), social (you can be ostracized by other people), or legal (you may be caught and punished).
We rely on government to define and enforce the more technical and complicated rules: various forms of fraud, cheating, theft, pollution, cartels, and so on. As well as the more obvious ones, like assault, rape, murder, and so on.
We also rely on government, specifically the court system, to arbitrate when there's a dispute, e.g. when two side have a contract and one of them decides to break it. (Criminals can't rely on this arbitration service, so they tend to resort to violence instead.)
4. Federal and provincial jurisdiction
The provinces run education and health care. That's most of what you need to know.
5. Political parties
Finally we get to the political parties.
Canada's a democracy, which means that power is transferred through elections (counting heads) rather than through violence (breaking heads). The country is divided into about 300 geographic areas called ridings; each riding has about the same number of voters. When there's an election, a number of candidates stand in each riding, and the voters there decide which candidate will be their representative ("Member of Parliament").
So what are the parties for?
In my experience, if you talk to four different individuals about their political opinions, you'll get four completely different views about what the government should be doing differently. In a democracy, you need some way to align all of these conflicting views, so that you can make collective decisions. I think of political parties (and political leaders) as playing a key role here: they come up with a platform that people can either support or oppose, depending on how attractive it is.
Political parties also serve to protect against wholly unsuitable candidates. Political scientists describe the US as having strong partisanship, but weak political parties; the Republican Party was too weak to stop Trump from claiming the presidential nomination.
Finally, political parties provide the opportunity for mass political participation on an ongoing basis, so that we're not just passive spectators who only participate by voting at election time. The parties are always looking for volunteers.
In a democratic system, power is based on mass participation: each election is like a tug-of-war, where each individual contribution may seem insignificant, but the cooperation of all the people on each side gives it tremendous power. The parties are a way for like-minded people to cooperate with each other.
So what do the parties stand for? Boiling it down to slogans:
- Conservatives - lower taxes, smaller government
- Liberals - good government
- NDP - justice for the oppressed, support for workers
Joseph Heath has a more detailed explanation of the difference between left (NDP), right (Conservatives), and centre (Liberals).